Abstract
We review what is currently known about the gluon Sivers distribution and what are the opportunities to learn more about it. Because single transverse spin asymmetries inp↑p→πXprovide only indirect information about the gluon Sivers function through the relation with the quark-gluon and tri-gluon Qiu-Sterman functions, current data from hadronic collisions at RHIC have not yet been translated into a solid constraint on the gluon Sivers function. SIDIS data, including the COMPASS deuteron data, allow for a gluon Sivers contribution of natural size expected from largeNcarguments, which isO(1/Nc)times the nonsinglet quark Sivers contribution. Several very promising processes to measure the gluon Sivers effect directly have been suggested, which besides RHIC investigations, would strongly favor experiments at AFTER@LHC and a possible future Electron-Ion Collider. Due to the inherent process dependence of TMDs, the gluon Sivers TMD probed in the various processes are different linear combinations of two universal gluon Sivers functions that have different behavior under charge conjugation and that therefore satisfy different theoretical constraints. For this reason both hadronic and DIS type of collisions are essential in the study of the role of gluons in transversely polarized protons.
Highlights
The distribution of quarks and gluons in a proton that is polarized transversely to its momentum need not be left-right symmetric with respect to the plane spanned by the momentum and spin directions
Several other pp scattering processes to access the gluon Sivers function have been suggested over the past years: p↑p → jet jetX [64], p↑p → DX [34, 44, 65], p↑p → γX [66], p↑p → γjetX [66, 67], p↑p → γ∗X → μ+μ−X [66], p↑p → jetX (single transverse spin asymmetries in jet production measured at RHIC [68, 69] at forward rapidities show very small asymmetries, which is probably due to a cancellation among u and d quark contributions [70]), p↑p → πjetX [71], and p↑p → ηc/bX [39]
No hard constraints on the size of the gluon Sivers function exist apart from the positivity bound, the theoretical expectation from large Nc considerations favors a 30% gluon to quark Sivers ratio, which is still completely allowed by all semi-inclusive DIS (SIDIS) data, including the COMPASS deuteron data
Summary
The distribution of quarks and gluons in a proton (or any other spin-1/2 hadron) that is polarized transversely to its momentum need not be left-right symmetric with respect to the plane spanned by the momentum and spin directions. AN for π0 production at midrapidity has been measured by the PHENIX experiment in polarized pp collisions at RHIC and was found to be consistent with zero, for pT values below 5 GeV at the permille level and for higher pT values (up to 11 GeV) at the few percent level [21, 43] These data taken at √s = 200 GeV probe x values only down to x ∼ 0.006, where still a combination of Qiu-Sterman functions is expected to contribute. The authors conclude that “both models give tiny asymmetry due to the small partonic cross sections, so the form of the three-gluon correlation functions is not much constrained by the data in this region.” From this limited model study of both π0 and D production one would conclude that TG(f)(x, x) and TG(d)(x, x) are in any case small, a permille fraction of x times the unpolarized gluon distribution. At small x it becomes very important whether one discusses the f or d type contribution (see Section 5), which is an issue not addressed in the GPM studies of AN
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